This unique book is dedicated to the application of self-consistent methods to the solution of static and dynamic problems of the mechanics and physics of composite materials. The effective elastic, electric, dielectric, thermo-conductive and other properties of composite materials reinforced by ellipsoidal, spherical multi-layered inclusions, thin hard and soft inclusions, short fibers and unidirected multi-layered fibers are considered. The book contains many concrete results.…mehr
This unique book is dedicated to the application of self-consistent methods to the solution of static and dynamic problems of the mechanics and physics of composite materials. The effective elastic, electric, dielectric, thermo-conductive and other properties of composite materials reinforced by ellipsoidal, spherical multi-layered inclusions, thin hard and soft inclusions, short fibers and unidirected multi-layered fibers are considered. The book contains many concrete results.
1. Introduction; Self-consistent methods for scalar waves in composites;2.1 Integral equations for scalar waves in a medium with isolated inclusions; 2.2 The effective field method; 2.3 The effective medium method; 2.3.1 Version I of the EMM; 2.3.2 Version I1 of the EMM; 2.3.3 Version I11 and nT of the EMM; 2.4 Notes; Electromagnetic waves in composites and polycrystals;3.1 Integral equations for electromagnetic waves; 3.2 Version I of EMM for matrix composites; 3.3 One-particle EMM problems for spherical inclusions; 3.4 Asymptotic solutions of the EMM dispersion equation; 3.5 Numerical solution of the EMM dispersion equation; 3.6 Versions I1 and I11 of the EMM; 3.7 The effective field method; 3.8 One-particle EFM problems for spherical inclusions; 3.9 Asymptotic solutions of the EFM dispersion equation; 3.9.1 Long-wave asymptotics; 3.9.2 Short-wave asymptotics; 3.10 Numerical solution; 3.11 Comparison of version I of the EMM and the EFM; 3.12 Versions I, 11, and I11 of EMM; 3.13
1. Introduction2. An elastic medium with sources of external and internal stresses2.1 Medium with sources of external stresses2.2 Medium with sources of internal stresses2.3 Discontinuities of elastic fields in a medium with sources of external and internal stresses2.4 Elastic fields far from the sources2.5 Notes3. Equilibrium of a homogeneous elastic medium with an isolated inclusion3.1 Integral equations for a medium with an isolated inhomogeneity3.2 Conditions on the interface between two media3.3 Ellipsoidal inhomogeneity3.4 Ellipsoidal inhomogeneity in a constant external field3.5 Inclusion in the form of a plane layer3.6 Spheroidal inclusion in a transversely isotropic medium3.7 Crack in an elastic medium3.8 Elliptical crack3.9 Radially heterogeneous inclusion3.9.1 Elastic fields in a medium with a radially heterogeneous inclusion3.9.2 Thermoelastic problem for a medium with a radially heterogeneous inclusion3.10 Multi-layered spherical inclusion3.11 Axially symmetric inhomogeneity in an elastic medium3.12 Multi-layered cylindrical inclusion3.13 Notes4. Thin inclusion in a homogeneous elastic medium4.1 External expansions of elastic fields4.2 Properties of potentials (4.4) and (4.5)4.3 External limit problems for a thin inclusion4.3.1 Thin soft inclusion4.3.2 Thin hard inclusion4.4 Internal limiting problems and the matching procedure4.5 Singular models of thin inclusions4.6 Thin ellipsoidal inclusions4.7 Notes5. Hard fiber in a homogeneous elastic medium5.1 External and internal limiting solutions5.2 Principal terms of the stress field inside a hard fiber5.3 Stress fields inside fibers of various forms5.3.1 Cylindrical fiber5.3.2 Prolate ellipsoidal fiber5.3.3 Fiber in the form of a double cone5.4 Curvilinear fiber5.5 Notes6. Thermal and electric fields in a medium with an isolated inclusion6.1 Fields with scalar potentials in a homogeneous medium with an isolated inclusion6.2 Ellipsoidal inhomogeneity6.2.1 Constant external field6.2.2 Linear external field6.2.3 Spheroidal inhomogeneity in a transversely isotropic medium6.3 Multi-layered spherical inclusion in a homogeneous medium6.4 Thin inclusion in a homogeneous medium6.5 Axisymmetric fiber in a homogeneous media7. Homogeneous elastic medium with a set of isolated inclusion7.1 The homogenization problem7.2 Integral equations for the elastic fields in a medium with isolated inclusions7.3 Tensor of the effective elastic moduli7.4 The effective medium method and its versions7.4.1 Differential effective medium method7.5 The effective field method7.5.1 Homogeneous elastic medium with a set of ellipsoidal inclusions7.5.2 Elastic medium with a set of spherically layered inclusion7.6 The Mon-Tanaka method7.7 Regular lattices7.8 Thin inclusions in a homogeneous elastic medium7.9 Elastic medium reinforced with hard thin flakes or bands7.9.1 Elastic medium with thin hard spheroids (flakes) of the same orientation7.9.2 Elastic medium with thin hard spheroids homoge neousl distributed over the orientations7.9.3 Elastic medium with thin hard unidirected bands of the same orientation7.10 Elastic media with thin soft inclusions and cracks7.10.1 Thin soft inclusions of the same orientation7.10.2 Homogeneous distribution of thin soft inclusions over the orientations7.10.3 Elastic medium with regular lattices of thin inclusions7.11 Plane problem for a medium with a set of thin inclusions7.11.1 A set of thin soft elliptical inclusions of the same orientation7.11.2 Homogeneous distribution of thin inclusions over the orientations7.11.3 Regular lattices of thin inclusions in plane7.11.4 A triangular lattice of cracks7.11.5 Col
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